Start by guessing some of the "big" countries, eg USA, Russia, Australia etc. You're pretty much guaranteed to get one right pretty quickly and that would give you a starting point. I like this quiz idea!

I'm curious what shape this would actually be on a globe. I assume it would not be a circle anymore, right? Along those lines, it would be cool to have a quiz like this where the map shown is actually the border of a hemisphere as seen when looking at a globe -- the projection would be different and might make it more of a challenge. That being said, this is a great quiz!